What is the significance of the name "Jehovah”?
Jehovah speaks of “the self-existent God of the covenant”. God revealed himself to Moses, from the burning bush, as Jehovah; although the name Jehovah appears before this in Scripture, it is unlikely that Moses wrote any of the Old Testament until after the experience at the burning bush.
Therefore, this is likely the first revelation to man of this majestic name. Here the one true God is clearly emphasizing to Moses his self-existent, unchanging, autonomous nature.
He is not the "I was" or the "I will be" but the always and unaffected "I AM."
In Exodus 3:14, the “I AM THAT I AM” comes from the word yhwh (Hebrews did not include vowels in their words) or jhvh. Some have filled in the vowels differently, or gone with the slightly different spelling, resulting in the name Yahweh.
We obviously do not know how it was actually pronounced, since the vowels were not included and since they did not say the name Jehovah anyway for fear of breaking the 3rd commandment. The Jewish leaders misapplied Leviticus 24:16 to say that even mentioning the name of God was a capital offense. Thus, when Jesus called himself the “I AM” in John 8:58, the Jews wanted to stone him for at least two reasons: first, because he was pronouncing the divine name and, second, because he was claiming to be the I AM! Jehovah, we might say then, is the personal name of God (like "George Washington"), while many of the other titles given him (e.g. Lord, Almighty, the Most High, etc.) are appellative titles or names (like "President").
Other names are, in the Old Testament, often attached to Jehovah in order to emphasize some attribute of the one true God -- Jehovah Avinu (the LORD our Father), Jehovah Sabaoth (the LORD of hosts), Jehovah Jireh (the LORD will provide). Wherever this name appears in the A.V. it is distinguished from other words translated as “Lord” by spelling it out in small capitals: LORD.
Therefore, it is still given a distinguished place as the name by which God revealed himself first and foremost to his people. “The name of the LORD is a strong tower: the righteous runneth into it, and is safe” (Proverbs 18:10).
Recommended Resources: We have an entire category in our Resource Center devoted to The Names of God.